Note that the DSW is not the same as in the case of an exact step, the
classical Gurevitch-Pitaevski problem [1]}. But one can for
instance verify that this is the correct solution by considering a
finite step smoothed out at both sides,
\(u(x,0) ={\left\lbrace \begin{array}{ll}1 & x_{0}<x<0 \\\exp (-x^{2n}) & x\ge 0\\\exp (-(x-x_{0})^{2n}) & x\le x_{0}\end{array}\right.}\) 
